What is an Infinite Series?

An infinite series is a sum of infinitely many terms. It is a mathematical concept that involves adding up an infinite sequence of numbers or terms. Each term in the series contributes to the total sum, and the sum can be finite or infinite.

Types of Infinite Series

There are different types of infinite series, including arithmetic series, geometric series, harmonic series, and power series. Each type has its own unique characteristics and properties that govern how the series behaves.

Convergence and Divergence

One of the most important aspects of infinite series is determining whether they converge or diverge. A series converges if the sum of its terms approaches a finite value as more terms are added. Conversely, a series diverges if the sum of its terms does not approach a finite value.

Applications of Infinite Series

Infinite series are used in various fields such as physics, engineering, and economics to model and solve problems involving continuous quantities. They are also fundamental in calculus for functions that can be represented as power series.

Understanding infinite series is crucial in advanced mathematics and has practical applications in various real-world scenarios.